DSP doesn't work like that, as in a higher quality chip won't provide different results than a worse quality chip, provided they run the same algorithm (same filters). Of course, the lower quality chip would have to be fast enough to run said algorithm/filters, otherwise nothing will work at all (not related to quality), or an algorithmic change would be required to make it still work. It's not like a better/worse DAC or amp that can have better or worse signal/noise ratio. Plus we don't even know if Dirac runs on the same DSP chip as Audyssey or not (would be economic if they did, but it's not necessarily possible/simple), plus we don't know if Dirac even requires more filter processing power than Audyssey (in fact, Dirac is supposedly more "economic" with how it uses filters).
Basically, room correction (and any DPS) is done on the digital domain, and its quality will be as good as the DSP algorithms used, and no extra noise can be added except the one added by flaws in the algorithm (or simplifications that needed to be done in order to make it run on slower hardware, which probably won't be the case here).
Whatever Dirac actually does/doesn't do much better than XT32 remains theoretical at this point. There have yet to be an actual test that proves any advantages of Dirac. Dirac with DLBC is a different beast, though, as it has capabilities that you can't get elsewhere (only MSO comes close, but that can usually be applied to subs only as you normally don't have the DSP required to apply it to your speakers, while DLBC applies to mains as well).